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Bimetallic Strip Bending Angle

  1. Jan 27, 2009 #1
    Hi! There is a thermodynamics problem which I seem to be able to understand, yet unable to solve. If someone can me with it I would appreciate it.
    1. The problem statement, all variables and given/known data
    A Bi-metallic strip is straight at T= T0. It curves as it is heated up due to unequal expansion of two metals. The strip is made up of iron (a = 1.2e-5) and zinc (a = 3.1e-5). The question asks to calculate the bending angle when the original length of the strip is 100mm and with thickness of 1 mm.


    2. Relevant equations
    The linear expansion equation: L = L0(1 + a(T2 - T0))


    3. The attempt at a solution
    The substituted equations: LI = (100)(1 + (1.2e-5)([tex]\Delta[/tex]T)
    LZ = (100)(1 + (3.1e-5)([tex]\Delta[/tex]T)

    From here I use the formula s = r[tex]\theta[/tex]
    and get [tex]\theta[/tex] = (3.8e-3)([tex]\Delta[/tex]T)

    I am not sure how to proceed from here because the question asks for a numerical answer but that seems impossible without the temperatures given.
     
  2. jcsd
  3. Jan 27, 2009 #2

    LowlyPion

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    Homework Helper

    Welcome to PF.

    If they give no temperature rise, then leave your answer in terms of ΔT as you have.
     
  4. Jan 27, 2009 #3
    Thanks. I guess I will leave it as an expression.
     
  5. Feb 1, 2009 #4
    Poptor, eh?
     
  6. Feb 1, 2009 #5
    Sorry for the double-post, but also.. I don't understand your solution.

    What does s=r*Theta have to do with this question.. and how does that lead to your solution?
     
  7. Feb 1, 2009 #6

    LowlyPion

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    The displacement of the end is given by the angle times the radius for small angle displacements.
     
  8. Feb 1, 2009 #7
    Oh.. what exactly is the radius in this question?
    I guess it's just that he said:

    3. The attempt at a solution
    The substituted equations: LI = (100)(1 + (1.2e-5)(LaTeX Code: \\Delta T)
    LZ = (100)(1 + (3.1e-5)(LaTeX Code: \\Delta T)

    From here I use the formula s = rLaTeX Code: \\theta
    and get LaTeX Code: \\theta = (3.8e-3)(LaTeX Code: \\Delta T)


    I sense a really big logic gap missing..

    Otherwise, I thought the appropriate formula was:

    Theta = length / thickness * (a1 - a2)*(T2-T1)

    Where a1 and a2 are the expansion coefficients, and T2 and T1 are temperatures.

    Excuse my ignorance, and thanks for the help.
     
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